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We show how open strings cease to propagate when unstable D-branes decay. Theinformation on the propagation is encoded in BSFT two-point functions forarbitrary profiles of open string excitations. We evaluate them in tachyoncondensation backgrounds corresponding to (i) static spatial tachyon kink (=lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i)the propagation is restricted to the directions along the tachyon kink, whilefor (ii) all the open string excitations cease to propagate at late time andare subject to a collapsed light cone characterized by Carrollian contractionof Lorentz group.Comment: 19 pages, published version (typos corrected, a reference added

Brane Decay and Death of Open Strings